Saturday, March 17, 2007

math(s)

As promised in the comments of my last post, this post pulls together and expands upon discussions that have come up more than once in comments on other posts and e-mails to me. Back in July, Ahab wrote:

I was castigated recently by a Brit for the nonsensical nature of saying math when the long form is mathematics, so any explanation you can provide on that front would certainly put my mind to rest.

Castigation is common on the math/maths issue, and the castigation is usually British to American. So, I'm going to castigate a bit in the other direction, because there's absolutely no reason why maths should be considered to be more correct than math.

The castigation usually goes: "Mathematics is plural, so maths needs its -s." It's a logic based on a false (AmE) premise/(BrE often) premiss. Just because there's an -s at the end of mathematics doesn't mean it's plural. The suffix -s is homonymous. Homonymy is when the same lexical forms (i.e. words or affixes) have unrelated meanings/functions. That is to say, it's when two words/affixes just happen to be pronounced/spelt the same. So, can is a homonymbecause either it can refer to a kind of container (can of Coke) or it can be a modal verb (I can go). Those two cans are completely unrelated. Similarly, there are several suffixes with different meanings/functions that all coincidentally have the form -s:

suffix

function

example

-s

plural

one cup > two cups

-s

present tense, 3rd sg
verb agreement

I run > he runs

-s

adverbial marker

unaware (Adj) > unawares (Adv)

-s

noun marker

linguistic (Adj) > linguistics (N)

(I've left out the possessive suffix 's, because it has some complicated properties that aren't relevant here.)

How do we know that these are really different affixes, and not just the same affix doing a range of jobs? Partly we know from history. The plural -s comes from an Old English case suffix (-es or -as). The verb one has derived from the suffix -eth (or -ath) in earlier Englishes. The adverbial one is related to the possessive 's. And our friend the nominali{s/z}ing (=noun-making) suffix generally affixes to roots from classical Greek. (See comments for further discussion.)

These suffixes differ in their productivity -- that is, how regularly/predictably one finds them in contexts where they could, in principle, go. The first two are very productive--although there can be exceptions in which they are not used. That is, while -s is the most productive plural marker in English, it's not the only plural marker--we also have -(r)en in children and oxen and a zero (invisible) suffix on sheep and fish (one sheep, two sheep).

The last two in the table are not very productive at all, and the last one is the -s we find in mathematics. Because we have a very productive and common plural -s and a not so productive/common nominali{s/z}ing -s, people often mistake the less productive suffix for the more common suffix. This has raised such a debate in the field of folkloristics that no fewer than three articles in Journal of American Folklore have addressed the final -s in folkloristics. [See References, below.] In one, Bruce Jackson calls folkloristics a noun with 'no existence as a noun in the singular', but he's corrected by Dan Ben-Amos, who says that folkloristics is instead a singular noun with no existence in the plural. (Note that there is no *folkloristicses.)

How can we tell whether or not this -s is marking a plural in mathematics and folkloristics? We do so by seeing whether the words trigger plural behavio(u)r in other words in the sentence. A first test might be whether you can count mathematics (* means 'ungrammatical'):

*one mathematic

*two mathematics

*a mathematic

some mathematics

Mathematics doesn't work with numbers because it's not a countable noun, it's a mass noun. That is, it does not take plural marking because it is not the kind of thing one can or does count. Similar examples (without the confusing -s) on the end are cinnamon and boredom. Note that you don't talk of putting *cinnamons in your food (unless you're making the point that they are different types of cinnamon--which is a different matter), nor does one suffer *boredoms if the boredom happened at different times. Cinnamon and boredom are treated as masses with undistinguishable (or at least not-worth-distinguishing), and therefore uncountable, parts. If we want to make such words countable, we have to use another noun to do so: two teaspoons of cinnamon, three episodes of boredom. Similarly, you can have three theories of mathematics or three mathematics classes, but not *three mathematics.

The third person, singular present tense -s verb suffix (the second -s in the table above) provides another test of singularity. If the subject of a verb is singular, then the verb needs the -s (or the equivalent in an irregular verb like is or has), but if the subject is plural, it can't have the -s. So:

singular subject

plural subject

The idea pleases me.

The ideas please_ me.

Mathematics pleases me.

??Mathematics please_ me.

Now, some of you will say that Mathematics please me is what you'd say. This is the effect of the folk-belief that mathematics is plural; it has started to change how people use the word. We see the same kind of language-change due to misapprehension of the -s suffix in the short form maths. Math is the older form--the OED has examples back to 1847, but examples of maths only from 1911.

Another interesting point here is that you don't see the same kinds of abbreviations for other nouns with the nominali{s/z}ing -s. For example,when BrE or AmE speakers abbreviate linguistics, they tend to say ling. I've never heard anyone talk about the Lings Department.

Why is maths the exception here? It probably has something to do with the fact that it's a much more common word, especially since it refers to a school subject. Because it's more common, it's subject to more folk-reasoning about it and more spread of that folk-reasoning. It also requires more frequent abbreviation than less common (linguistics, folkloristics) and shorter (physics) similar words. So, someone along the line misunderstands it as plural, starts using the -s in the abbreviation, and perhaps making it agree with plural verbs, and it spreads. It carries on because the belief that -s on nouns is always a plural marker is a simpler belief to hold than that -s has different functions on different nouns.

Better Half has just run in from listening to A Prairie Home Companion, where he says that Garrison Keillor just said you do the maths. (The AmE expression is usually you do the math.) We met Keillor (if it counts as a 'meeting' to have a book signed and make a little chit-chat about being an American abroad) in Brighton a couple of years ago, and in many ways you could say he's not a typical AmE speaker (even though he certainly trades on his down-home midwesternism), since he's lived abroad at various points in his life. But do let me know if you're a Minnesotan who believes this is one of Keillor's actual down-homeisms.

Myself, I do tend to say maths in BrE company, but only because it's so painful not to. Can you imagine if I had to say all of the above every time I was unjustly castigated?

Postscript Since writing this blogpost, I was a part of this:

References
Ben-Amos, Dan. (1985) On the Final [s] in Folkloristics. The Journal of American Folklore, 98: 334-336

Hansen, Wm. F. (1987) A Note on the Final [s] in Folkloristics. The Journal of American Folklore, 100: 305-307.

Two other nice examples of -s confusion and mass/count noun confusion are peas(e) and corn.

Pease was originally a mass noun, like wheat or rye; the individual items didn't matter. But because it ended in an s-sound, it came to be thought of as a plural, and the unhistorical singular pea was created; the plural then came to be spelled peas. The nursery rhyme still (on both sides of the Pond) says Pease porridge hot, pease porridge cold, though, preserving the older mass form.

On the other hand, corn, a mass noun referring to the staple grain of any particular country (wheat in England, oats in Scotland) came to refer exclusively to Indian corn, or maize, in North America. However, even though nothing could look more countable than ears of maize, corn remains a mass noun over here, and to speak of individual items we must talk of ears of corn.

Telecom(s) is a slightly different issue--as your examples show, Dan, it often occurs when it's being used as a modifier of another noun--i.e. telecom(s) industry. While one can say telecommunications industry in either dialect, telecommunication industry is probably more likely to be said by an American than a Brit--see the previous discussion on drugs problem versus drug problem.

The other issue here is whether or not telecommunications is plural. It's not the non-plural -s from mathematics, and it can take a plural verb:

But, when it's referring to an industry, it can be treated as singular:

Telecommunications is a growing sector.?Telecommuncations are a growing sector.

Since it has a different -s suffix than mathematics, I wouldn't want to conclude straight away that it's the same phenomenon, but it may be that BrE is more accustomed to having -s at the end of clipped words (see also on nicknames here), thus when it has a choice of having an S or not, it's more likely to choose the S than AmE is.

So, it's a fairly complex issue, but part of what would need to be looked at is whether AmE speakers are saying telecom both in cases where they could have said telecommunications and in those where they'd say telecommunication. I'll bet you're right in assuming they do both. But the fact that the word is not a classic semantic plural (you often can't count the telecommunications that are referred to, means it's the kind of word on which a bit of variation isn't terribly surprising.

I don't think you can say the nominalizing -s comes from Classical Greek. Etymologically it is the English plural suffix. In Greek there is an adjective-forming suffix -ikos, and its neuter plural can be used to make a sort of collective, which remained grammatically plural in Greek. For example, ta phusika 'natural (things)' (whence Eng. physics) derived from phusis 'nature'. So ta mathematika 'things connected with learning' (whence mathematics). This pattern of denoting scholarly discipines with a pluralized (collective) adjective was calqued in English. But the syntax has changed, so that, as lynneguist says, -s in -ics is not now a plural suffix.

I think that in most cases, when one tries to use mathematics/maths with a plural verb, it becomes obvious that this is wrong, and that math(ematic)s cannot be plural. Maths are boring is obviously wrong. Mathsisboring, as every skuleboy kno.

Another word with a nominalising -s which often seems to be mistaken for a plural is politics, which is frequently and infuriatingly (to me, at least) used with a plural verb. Whenever I hear the phrase His politics are to the right of Genghis Khan I find myself shouting "No! You're wrong! His politics is to the right of Genghis Khan".

Historicity trumps. For example, the discussion of s cf. z always ends with a wistful sort of concession on the part of Her Majesty's subjects. Saying 'math is the older form - the OED has examples back to 1847, but examples of maths only from 1911' should produce the same result. I am going to try it with one of my most frequent critics.

This post has me trying to think of other -ics words that follow suit. Scholastics? Gymnastics? What about aerobics? That seems to be both singular and plural. My aerobic workout, doing my aerobics. Or is the latter a dodgy popularisation?

Hi Max--originally I had written 'it comes from classical Greek, kind of'--and I took out the 'kind of' because I didn't want to be asked explain my reasoning. :) I had thought that the 's' was a retro-Greek effect (based on something I'd read in one of the dictionaries), but I'm happy to go with it being based on the plural -s, as long as we're acknowledging that it's no longer acting as the productive plural -s. I'll make a slight change in the post, just to be less misleading.

Some of the other examples are very interesting, though. Politics I'd usually use with a plural verb, but gymnastics and aerobics with a singular.

Would you really use "politics" as a plural? "I like to read about politics, but I don't like to participate in them." Them?

In Australia, I think it is usually used as a plural in the stock phrase "one's politics" and its variants. I don't know if an Australian would use it as a plural in other contexts, but it would surprise me if an American would make it plural in any context. In fact, I don't think the phrase above would be used in at all, either as singular or as plural. For example, I would think that the sentence "I don't agree with his politics" would be naturally Americanized into something like "I don't agree with him politically" or "I don't agree with his political philosophy/point of view/ideas/..."

As for maths, I'm a professional American mathematician living in Australia, and I don't think I've ever heard a colleague use "maths" as a plural. On the other hand, mathematicians essentially always use the plurals "matrices" and "indices" where most people would use the regular forms. So we might be a bit old-fashioned when it comes to plurals.

Last, and in contrast to "politics", I did once hear an American mathematician use "mathematics" as something to be possessed ("Coleman's mathematics").

Here are some dated examples from the Oxford English Dictionary, of, first, mathematics, and then politics used as plurals and as singulars. Note especially several recent examples of politics as a plural, and not just in a "Possessive+politics" construction.

1712 R. Bentley Let. in Corr.(1842) II.449 Mathematicks was brought to that height, that etc..

1755 Man No. 35.3 Mathematics derives its accuracy‥from logic.

politics[from politic n. (see -ic suffix 2), after Middle French politiques, polliticques public affairs, government, also the title of Aristotle's treatise on politics (all late 14th cent.) and its models post-classical Latin politica, the title of Aristotle's treatise on politics (14th cent. in British sources), public affairs (1488 in a British source), and ancient Greek τὰ πολιτικά public matters, civic affairs. Cf. earlier POLITIC n.

With sing. or pl. concord. (App. with plural concord only until the early 18th cent. and thereafter freq. when a set of distinct principles, policies, or practices is in view.)

PLURAL1693 Humours & Conversat. Town 42 The Coffee-house Politicks are but Fewel to Factions.

1739 D. Hume Treat. Human Nature I. Introd. 5 Politics consider men as united in society, and dependent on each other.

You're right, James, as soon as I got off the computer and onto the train, I reali{s/z}ed that my "politics is plural to me" claim only applied to possessed politics:

Her politics are creepy.butPolitics is an interesting way to make a living.

But, keeping with Max's/the OED's observation that not all plural politics(es) are possessed, it does vary a bit by context. Now--the question is, has someone studied this in depth to let us know what determines which "one sounds right" where? Sounds like a great project for a student...

What is weird (for me) is that mathematics, while it can be possessed, sounds neither singular nor plural to me--that is, it sounds weird no matter which verb I use:

??Her mathematics are questionable.??Her mathematics is questionable

If this involved adding up, I would just avoid mathematics and would instead say arithmetic. But notice that it's no problem with the abbreviated form of mathematics:

(AmE) Her math is questionable.(BrE) Her maths is faulty (from here)or(BrE) Let's hope her maths are better than Dubya's. (from here)

(Incidentally, I got about 8 times more hits for "her maths is" over "her maths are", but not all of the "her maths is" examples had the same structure as needed to compare these two--e.g. "the trouble with her maths is..." doesn't count. I've not got the energy/time to go through them all now to see which one is more popular.)

Thanks for your eagle-eye, Doug. I actually started using spelt before I moved to the UK, in part out of keyboard laziness, in places in which I pronounce it with a /t/ instead of a /d/ at the end--which seems to mostly be when I use it in the participial form. The first time I used it here on SbaCL I checked my dictionaries, since I am aware that it's not a common AmE form--but they didn't mark it as dialectal--just as an alternative spelling. So (given my avowed laziness) I just started using it all over the blog without marking it. But since I mark other things that are dialectal preferences rather than hard-and-fast presences/absences, you're right; I should mark it. Will try to remember to do it from now on--or else will lazily avoid it by inventing a new word. How about orthographed?

Politics seems to be an interesting anomaly. The singular form "His politics is..." sounds hideous to my (mainly BrE) ear. Absolutely non-grammatical. But at the same time it's clearly not a plural on its own - "Politics is boring" is perfectly grammatical whereas "Politics are boring" is unacceptable. I wonder how Chomsky would explain that.

"On the other hand, mathematicians essentially always use the plurals "matrices" and "indices" where most people would use the regular forms."

Arguably "-ices" is the regular form, using Latin grammar for (almost?) explicitly Latin words. Also I'd argue that "most people" using the plural of matrix are mathematicians.

It is regular if everything more than one syllable that ends with -ix gets an -ices plural (now I haven't checked if this is a true statement for English). 'Regularity' doesn't have to mean 'all the same'...

Regarding problems with the Google search for "her mathematics is/are":

Are there automated ways of weeding out the irrelevant examples, ones like "the trouble with her maths is..."? It would be great to have a Google with grammar. It's probably too much to ask for, but when I go through them myself, I feel like a computer could do it. And there are lots of smart people out there.

But in "the trouble with her mathematics is", the is agrees with trouble, not mathematics--so that wouldn't be a good indicator of whether mathematics is plural. I agree that it's usually possible to find bigger contexts in order to reduce the grammatical ambiguities of a search string, but I haven't been successful in finding one that gets any hits whatsoever for this problem.

I just had a peek at the LOB/FLOB corpora (2m words of BrE), and found 39 instances of mathematics but only one with a singular, present tense verb (which was singular: isn't). None of the cases of maths was the subject of a verb, so no evidence there.

In formal English at least, codex --> codices, index --> indices, matrix --> matrices, appendix --> appendices, dominatrix --> dominatrices. In fact, the only exceptions I can think of off the top of my head, ironically enough, are prefix and suffix.

Lynnguist, I think that was James' point, to have a means of google searching whereby such examples (in which the verb inflects for something other than maths) don't skew the results.

Regarding the original point of your post, I don't think your explanation of this particular -s suffix clearly shows one way or another that either math or maths is correct. You could say the suffixation occurs post-clipping, in which case maths would be the correct one. Phonotactically speaking, I have an issue with θ-final words, I think... With seems to be fine, but math doesn't.

I'd say prefix and suffix are a bit funny because (unlike the other ones here), the ix is part of another one-syllable morpheme -fix. But, whatever, I wasn't actually trying to make the case that it was regular--just to point out that just because something is part of a smaller pattern doesn't mean that its pattern isn't 'regular'.

There are plenty of θ-final words that I have no problems with and I don't know why math sounds so very bad to me. It could be a vowel quality thing, remember that my dialect differentiates the /a/ in path and bath from /æ/ in math. Perhaps I don't have a problem with with, bath or path because they're the only options, whereas I have maths as an option, so math is... dispreferred (some sort of dialectal optimality theory?). Maybe I'm subconsciously rationalising a dialectal disliking of math by appealing to phonology.

A philosophy colleague with whom Blogger didn't want to cooperate, sent the following comment by e-mail (and I thought it was interesting, so I copy it here):

"Just two little things. First, a number of philosophers irritatingly describe a particular type of metaphysical theory as 'a metaphysic', where I would say 'a metaphysics' (by analogy with 'the new physics', or 'Newtonian physics', both of which I take to be singular).

If "data" and "criteria" complete the transition from plural to singular, they will be following in an hono(u)rable tradition of English words such as "truce" and "bodice", which were originally the plurals of "true" and "body" respectively. There's also "dice", which is generally used as a singular in the UK but in the US widely retains its historical role as the plural of "die".

(1) My first job was with the External Telecommunications Executive of the General Post Office (usually G.P.O.); when the Telecommunications arm of the latter became "British Telecom". I was staggered : they had dropped the final /two/ letters of "Telecomms", the until-then customary <Br.E> abbreviation of "Telecommunications". Needless to say, I still refer to them as "British Telecomms" if ever I have need to spell out "B.T.".

(2) Like Jangari, I have great difficulty in making the sound of "math"; having said "maths" for well over fifty years, if I try to make the sound of "math" my mouth feels as if I have tried to swallow chalk dust !

Am I wrong in saying that "math" and "maths" sound almost identical when pronounced? If so, could this be what reinforces the continued difference in spelling? Each person hears whatever he or she thought the spelling was.

I thought we thought it was plural become it comes from the Greek mathēmatiká through the Latin mathematica, but this is very far outside of my expertise!

On the use of maths as a plural, a commenter to my blog post on the subject pointed out that the early use I found through Google Books (two examples from 1916) used it as a plural: "these beastly maths" and "aren't maths beautiful?" (links in my blog post). To my mind these sound wrong, but a search for "maths is" found its first hits in the late 1930s, even though a previous comment here points out early examples of "mathematics" being used as both plural and singular. (Not that Google Books is a comprehensive or reliable way to search these things.)

On similar forms, a commenter on my post pointed out that American English seems to have no use of "stat" for "statistics", preferring, as British English does, to use "stats". Mind you, "statistic" is used as the singular in the way "mathematic" isn't.

On the lack of a "mathematic" singular, I'm interested that apparently the French les mathématiques has a singular form la mathématique.

The lack of the noun 'mathematic' should be enough to show that the word 'mathematics' is not a plural noun. Instead, 'mathematics' (as a noun) should be thought of as logically equivalent to the phrase "the study of mathematics" for which a given verb would be conjugated according to the singular noun 'study'. Therefore, we should use the verb "is" with the subject noun 'mathematics'. In the words of Einstein, "Mathematics is the poetry of logical ideas."

Various thoughts:1) My concise OED gives mathematics as a plural noun without any alternative possibility.2)I think here the French language can shed an interesting light on the discussion.(Full disclosure: I confess to my sins, I'm French).-Because French has different forms of the definite article for the singular (le/la) and the plural (les), there is almost never any question/doubt about the number of the noun for mathematics.- In French the discipline taught in every school is "les mathématiques" (plural). It is commonly abreviated into les "maths" (definitely plural too).- The noun "mathématique" can be used in the singular (rarely) as a synonym of the plural form or to refer to a rigorous deductive reasoning.- When the singular-as-synonym-of-the-plural is used, it is either in an affectedly archaic manner or (mainly) by modern mathematicians to emphasise the fact that applying a deductive method of reasoning to abstract objects whatever the objects are (numbers, shapes, groups of numbers, etc) is a single discipline as opposed to the idea held by the ancients that calculus, geometry, algebra, etc, were distinct sciences collectively qualified as "mathematical".For details http://www.cnrtl.fr/definition/math%C3%A9matique- This ancient way of thinking about different areas of maths is the reason (IMO) why, while most other subjects and disciplines are singular in French, maths isn't, in the common use. linguistics=linguistique, physics=physique, etc.- You will tell me, and you'd be right, that the fact the French do so doesn't mean it is a rule universally acknowledged. But a lot of words in the English language come from Latin via French or directly from French. So I'd bet let's say not a kidney but definitely a toe that for some time around and after the time the word mathematics appeared in English, a French influence could be felt.3) Even if we dismiss the French-as-font-of-all-truth hypothesis as too tainted by misplaced patriotism, isn't it possible that the reason why the word mathematics resists the process which saw other subject substantives evolve from plural to singular, like physics or linguistics, (I am going here for the originally plural because of the influence of Greek and Latin's collective/neuter plural science names hypothesis here) is that this ancient idea of different mathematical fields has been there from the beginning in English and endures to this day?4) Is it possible that "math" without an s, while being plural all along, isn't a misspelling: as an abreviation, it might not have to show the s at the end? I am not an English native speaker, so it's just an idea...5) Oh dear! This is a looong post and, no doubt, badly written. Sorry.

A side thought, but one I've had often. English always seems to me a developed creole, its grammar remarkably simplified by its mixing with French, so that it doesn't have declensions or much conjugation of verbs or much of anything to mark the forms of words. Even plurals are sometimes indistinguishable from the singular forms of words.

All of that is preface.

But the one thing that usually marks a word is what? A terminal s. Nothing else. It shows our plurals, does most of the work of conjugation for us, does the other marking you've pointed out. And I think it does one more thing.

It is used at the end of names. I used to interpret that what it did was mark the vocative case. Because we would use the work Jacks (for Jackie) and Neens (for Nini) for my sisters' names, but usually only when we spoke to them directly. I've run across enough examples now that I think it really only marks names and is meant as the marker of a diminutive or familiar form of a name. So it demonstrates one's closeness to or affection for someone.

If you have any thoughts on this, I'd be happy to hear them. I'm not a linguist, just a desultory thinking on language.

"You do the arithmetic" would be a perfectly good compromise between the two and would probably more accurately convey what one was attempting to say. My understanding is that "arithmetic" is the actual operation while "Mathematics" is the theoretical science involved. "Connect the dots" is another way of saying the same idea.

Re: math/maths. I admit to not being anywhere near as schooled in the linguistic art as you, but if I might offer my ignorant insight, I've been taught to use maths vice math depending on context under the perhaps incorrect instruction that math may generally mean and be interchangeable for arithmetic, however there is more to mathematics than conducting a simple commerce in arithmetic, and mathematics is a shorthand for the various branches of mathematics, whereas math in the singular is really a short version of 'the branch of mathematics involving counting / arithmetic'.

That's what I would call post-hoc rationalization of the difference. There's a lot of that when people try to come up with reasons for linguistic differences. Usually the reason for the difference is 'it started out this way in this place, and it stuck'.

I also think that it is interesting that, at least to Americans born in the 80's and later (I'm not sure about earlier), Math is a countable thing. For example, I took Algebra, Pre-calculus, and Geometry classes. In each I learned one type of math, and in the year I took Algebra and Geometry at the same time I took two types of maths at once. When I got to university in the UK I found out me friends had takes A levels in maths or further maths where they learned things as one big lump. For me Math was always a word for a type of class that was separate and distinct from mathematics as the branch of learning that was taught within it.

If "mathematics" is the noun formed from an adjective, then why would I never use "mathematic" as an adjective? (I'd use mathematical, as in, "mathematical reasoning"). However I would use "arithmetic" as an adjective, as in "arithmetic series".

If "mathematics" is the noun formed from an adjective, then why would I never use "mathematic" as an adjective? (I'd use mathematical, as in, "mathematical reasoning").

The OED suggests that mathematics was a coinage in European languages based on physics etc, rather than a direct borrowing from Greek. So while the classical Greek word that gave rise to physics was indeed a noun based on an adjective, this is not true of mathematics

However I would use "arithmetic" as an adjective, as in "arithmetic series".

This would seem to be a relatively recent thing. The OED quotes:

1954 T. W. Chaundy et al. Printing of Math. 64 In changing practice some mathematical terms have shortened. Thus we say ‘convergence’ rather than ‘convergency’; ‘algebraic’, ‘geometric’ generally replace ‘algebraical’,‘geometrical’, and even ‘arithmétic’ (so accented), can be an adjective as in ‘arithmetic mean’.

They give examples of adjective arithmetic that are earlier, but this quote seems to signal the start of a more general use.